Reachability-Aware Time Scaling for Path Tracking

2026-03-31

AI Summary

This work addresses the single-step reachability issue arising in planar double-integrator systems when tracking high-curvature, collision-free paths under acceleration constraints. To resolve this, the authors propose a reachability-aware time-scaling mechanism that integrates offline spline-based path fitting with an online pure-pursuit architecture. While preserving the original path geometry, the method computes offline acceleration margins to generate a velocity scaling profile, which then informs a reachability-guided quadratic programming tracker. This tracker dynamically adjusts the velocity profile in real time to satisfy system dynamics constraints. Experimental results demonstrate that the proposed approach enables stable and dynamically feasible tracking of complex paths under bounded velocity and acceleration limits.

Abstract

This paper studies tracking of collision-free waypoint paths produced by an offline planner for a planar double-integrator system with bounded speed and acceleration. Because sampling-based planners must route around obstacles, the resulting waypoint paths can contain sharp turns and high-curvature regions, so one-step reachability under acceleration limits becomes critical even when the path geometry is collision-free. We build on a pure-pursuit-style, reachability-guided quadratic-program (QP) tracker with a one-step acceleration margin. Offline, we evaluate this margin along a spline fitted to the waypoint path and update a scalar speed-scaling profile so that the required one-step acceleration remains below the available bound. Online, the same look-ahead tracking structure is used to track the scaled reference.

Problem

• path tracking
• reachability
• acceleration constraints
• time scaling
• collision-free path

Innovation

• reachability-aware
• time scaling
• path tracking
• quadratic programming
• acceleration constraints